It’s a usage I encounter now and then – always from a British source, as at the end of Time Bandits: “Left the Sunday joint cookin’ all night, did we?” (In America the word “joint” can mean several different things, but it never means a cut of meat.)
Come to think of it, what’s a Sunday joint? Is it British custom to have a family feast on Sundays?
It usually means beef, and it can be any cut of beef, but rib or sirloin is most common. It’s then served as the main part of a “traditional” Sunday roast, consisting of roast beef, roast potatoes (plus, if you’re a member of my potato-obsessed family, a couple of other kinds of potato as well), Yorkshire puddings, gravy and a couple of veg. There’d normally be a sweet pudding afterwards - creme caramel or sherry trifle were favourites in my family, but those aren’t “traditional”.
Once upon a time, it was a way of getting the whole family together, on the one day no-one would be working, usually after church. The leftovers would then form the basis of the next couple of meals - Bubble and Squeak from the veggies, cottage pie from the meat, soup from the bones, etc.
Sunday roasts are more commonly eaten in pubs these days than cooked at home, though I cook them occasionally - normally when we’ve got friends round, as it’s too much for two. I cheat and buy ready-made frozen Yorkshire pudding, but I make cracking gravy and roast spuds.
It’s evil.
Don’t touch it.
Roast beef is the traditional British Sunday lunch but I don’t think the Sunday “joint” necessarily implies beef. It could be leg or shoulder of lamb or leg, shoulder or loin of pork. Traditionally it would have had the bone in but these days probably boned and rolled. Sunday lunch could also be roast chicken but I don’t think I would call that a “joint”.
Jennyrosity’s description of the trimmings to go with the beef are spot on (except I would insist on horseradish sauce with the beef) but for the lamb and the pork you have got to have mint sauce and apple sauce respectively - yum 
Chicken has to have sage and onion stuffing and bread sauce. Almost all pubs will do a fixed price roast dinner on Sundays - it may be the only thing they do on Sundays, normally with a choice of two or three meats. (I blame this for the sad degeneration of British culture where people have yorkshire pudding with lamb and stuffing with beef :smack: ).
We still do a roast most Sundays but more early evening than lunchtime when the whole family is in from whatever they’ve been doing during the day. I cook the yorkies from scratch, very easy really and I like to see how much the individual puddings can puff up!
And, in case it’s not apparent from context, “Sunday joint” because, only a generation or two back, meat was expensive enough that a roasting cut was a once-a-week luxury, the remainder to be eaten cold on Monday and ground up in rissoles on Tuesday. It’s still fairly unusual to go to all the trouble of cooking a roast plus all the extras on weekdays, even now they’re more affordable.
Stole my line.
<Touches it>
I thought “pudding” was the British term for American “dessert”.
We have both sweet and savory puddings eg: treacle pudding = sweet, steak and kidney pudding = savory.
According to my link, Yorkshire puddings can be served as a sweet dish with syrup or jam. I’ve never tried them like that, but I guess it would work - they’re basically just baked pancake batter.
booooom!